Stacking Buttercakes - Are They Too Heavy?

AHello all, complete newby here! So I'm making a 3 tiered wedding cake. Each tier is made of 2 x buttercakes of different colours, to give an overall rainbow effect. Each individual cake is about 5cm (2 inches) high, so each of the 3 tiers will be 10cm (4 inches) high. I'm making 6, 8 and 10 inch tiers.... Question finally... Will the 2 cakes in each tier be too heavy on each other? Ie: will one 10 inch cake of 2 inch depth resting on another to make one tier, end up sinking? So should I dowel support within each tier? Thank you muchly! :D